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A226547 Number of squares in all tilings of a 4 X n rectangle using integer-sided square tiles. 3
0, 4, 25, 98, 386, 1402, 4938, 16936, 57020, 189172, 620397, 2015456, 6496391, 20801576, 66231279, 209847980, 662049349, 2080850248, 6518383898, 20358327362, 63413001935, 197042859318, 610922240964, 1890331512546, 5838350817615, 18001432735438, 55417333344241 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,2,-12,-11,2,10,6,-1,-2,-1).

FORMULA

G.f.: (x^5+6*x^4-8*x^3-10*x^2+9*x+4)*x/((x+1)^2*(x^4-3*x+1)^2).

a(n) = 4*a(n-1) + 2*a(n-2) - 12*a(n-3) - 11*a(n-4) + 2*a(n-5) + 10*a(n-6) + 6*a(n-7) - a(n-8) - 2*a(n-9) - a(n-10) for n>9. - Colin Barker, Jun 07 2020

PROG

(PARI) concat(0, Vec(x*(4 + 9*x - 10*x^2 - 8*x^3 + 6*x^4 + x^5) / ((1 + x)^2*(1 - 3*x + x^4)^2) + O(x^30))) \\ Colin Barker, Jun 07 2020

CROSSREFS

Column k=4 of A226545.

Cf. A054856.

Sequence in context: A323967 A195509 A027949 * A264167 A152215 A231175

Adjacent sequences:  A226544 A226545 A226546 * A226548 A226549 A226550

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jun 10 2013

STATUS

approved

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Last modified September 25 20:01 EDT 2021. Contains 347659 sequences. (Running on oeis4.)